NMR for equilateral triangular geometry under conditions of surface relaxivity - Analytical and random walk solution

Transport in Porous Media

Volumn 69, Issue 1, 2007, Pages 33-53

  Finjord, Jan ^b   Hiorth, Aksel ^a   a Lad, Unn H ^a   Skjæveland, Svein M ^b  

^a RF Rogaland Research   (Norway)

^b UNIVERSITY OF STAVANGER   (Norway)

Author keywords

Analytical; CPMG NMR; Diffusion; Equilateral triangle; Random walk

Indexed keywords

COMPUTATIONAL GEOMETRY; DIFFUSION; GREEN'S FUNCTION; MAGNETIC RELAXATION; MAGNETIZATION; SURFACE RELAXATION;

ANALYTICAL EXPRESSION; MAGNETIC GRADIENT; TRANSVERSE MAGNETIC RELAXATION;

NUCLEAR MAGNETIC RESONANCE;

COMPUTATIONAL GEOMETRY; DIFFUSION; GREEN'S FUNCTION; MAGNETIC RELAXATION; MAGNETIZATION; NUCLEAR MAGNETIC RESONANCE; SURFACE RELAXATION;

ANALYTICAL METHOD; EXPERIMENTAL STUDY; GEOMETRY; GREEN FUNCTION; MAGNETIZATION; NUCLEAR MAGNETIC RESONANCE; RANDOM WALK METHOD;

EID: 34250888807     PISSN: 01693913     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11242-006-9062-7     Document Type: Article

References (45)

1. Al-Mahrooqi, S., Grattoni, C., Muggeridge, A., Zimmerman, R., Jing, X.: Pore-scale modelling of nmr relaxation for the characterization of wettability. Paper presented at the 8th International Symposium on Reservoir Wettability, Houston, May 16-18, 2004
2. Bergman D., Dunn K., Schwartz L., Mitra P. (1990) Self-diffusion in a periodic porous medium: A of different approaches. Phys. Rev. E 51, 3393-3400
3. Brownstein K., Tarr C. (1979) Importance of classical diffusion in NMR studies of water in biological cells. Phys. Rev. A 19, 2446-2453
4. Brownstein K., Tarr C. (1977) Spin-lattice relaxation in a system governed by diffusion. J. Mag. Reson. 26, 17-24
5. Callaghan P. (1991) Principles of Nuclear Magnetic Resonance Microscopy. Oxford University Press, Oxford
6. Carr H., Purcell E. (1954) Effects of diffusion on free precession in NMR experiments. Phys. Rev. 94, 630
7. Freedmann, R., Heaton, N., Flaum, M., Hirasaki, G., Flaum, C., Hürlimann, M.: Wettability, saturation, and viscosity using the magnetic resonance fluid characterizing method and new diffusion-editing pulse sequences. SPE 77397, 2002 SPE Annual Technical Conference and Exhibition, San Antonio, September 29-October 2
8. Heaton, N., Freedman, R., Karmonik, C., Taherian, R., Walter, K., Depavia, L.: Application of a new-generation NMR wireline logging tool, SPE 77400, 2002 SPE Annual Technical Conference and Exhibition, San Antonio, September 29-October 2
9. van Dijke M., Sorbie K. (2003) Three-phase capillary entry conditions in pores of noncircular cross-section. J. Colloid Interface Sci. 260, 385-397
10. Helland, J., Skjæveland, S.M.: Physically based capillary pressure corelation for mixed wet reservoir from a bundle of tubes model. SPE 89428, 2004 SPE/DOE Fourteenth symposium on improved oil recovery, Tulsa, April 17-21
11. Helland, J., Skjæveland, S.M.: Three-phase mixed-wet capillary pressure curves from a bundle-of-triangular-tubes model. The 8th International Symposium on Reservoir Wettability, Houston, May 16-18, 2004
12. Howard J.J. (1998) Quantitative estimates of porus media wettability from proton NMR measurements. Magn. Reoson. Img. 16, 529-533
13. Hui M., Blunt M. (2000) Effects of wettability on three-phase flow in porous media. J. Phys. Chem. B 104, 3833-3845
14. Hürliman M., Venkataramanan L. (2002) Quantitative measurement of two-dimensional distribution functions of diffusion and relaxation in grossly inhomogeneous fields. J. Mag. Reson. 157, 31-42
15. Hürlimann, M., Venkataramanan, L., Flaum, C., Speier, P., Karmonik, C., Freedman, R., Heaton, N.: Diffusion-editing: New NMR measurement of saturation and pore geometry. The 2002 SPWLA Annual Logging Symposium, Houston, June 2-5
16. Jackson, M., Valvatne, P., Blunt, M.: Prediction of wettability variation and its impact on waterflooding using pore- to reservoir-scale simulation. SPE 77543, 2002 SPE Annual Technical Conference and Exhibition, San Antonio, September 29-October 2
17. Lisitza M., Song Y. (2002) Manipulation of the diffusion eigenmodes in porous media. Phys. Rev. B 65:172406
18. Marinelli L., Hürlimann M.D., Sen P.N. (2003) Modal analysis of q-space relaxation correlation experiments. J. Chem. Phys. 118(19):8927-8940
19. Mason G., Morrow N. (1991) Capillary behavior of a perfectly wetting liquid in irregular triangular tubes. J. Coll. Int. Sci. 141, 262-274
20. Matsumoto, M., Nishimura, T.: Dynamic Creation of Pseudorandom Number Generators, Monte Carlo and Quasi-Monte Carlo Methods 1998, pp. 56-69. Springer (2000)
21. Matsumoto M., Nishimura T. (1998) Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator. ACM Trans. Mod. Comp. Sim. 8, 3-30
22. Mccartin B. (2003) Eigenstructure of the equilateral triangle, Part I: the Dirichlet problem. SIAM Rev. 45, 267-287
23. Mccartin B. (2002) Eigenstructure of the equilateral triangle, Part II: the Neuman problem triangle. Math. Probl. Eng. 8, 517-539
24. Mccartin B. (2004) Eigenstructure of the equilateral triangle. Part III. The Robin problem. IJMMS 16, 807-825
25. Meiboom S., Gill D. (1958) Compensation for pulse imperfections in Carr-Purcell NMR experiments. Rev. Sci. Instrum. 29, 688
26. Mendelson K. (1993) Continuum and random-walk models of magnetic relaxation in porous media. Phys. Rev. B 47, 1081-1083
27. Mendelson K. (1990) Percolation model of nuclear magnetic relaxation in porous media. Phys. Rev. B 41, 562-567
28. Mitra P., Sen P., Schwartz L. (1993) Short time behavior of the diffusion coefficient as a geometrical probe of porous media pore geometries. Phys. Rev. B 47, 8565-8574
29. Morrow N., Mason G. (2001) Recovery of oil by spontaneous imbibition. Curr. Opin. Coll. Int. Sci. 6, 321
30. Piri, M., Blunt, M.: Pore-scale modeling of three-phase flow in mixed-wet system. SPE 77726, 2002 SPE Annual Technical Conference and Exhibition, San Antonio, September 29-October 2
31. Press, W. et al.: Numerical Recipes in C. Cambridge (1992)
32. Price W. (197) Pulsed-field gradient nuclear magnetic resonance as a tool for studying translational Part 1. Basic theory. Concepts Magn. Reson. 9, 299-336
33. Price W. (1998) Pulsed-field gradient nuclear magnetic resonance as a tool for studying translational Part II. Experimental aspects. Concepts Magn. Reson. 10, 197-237
34. Radke, C., Kovscek, A., Wong, H.: A pore-level scenario for the development of mixed wettability. SPE 24880, the 1992 Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, Washington, DC, October 4-7
35. Song Y. (2000a) Detection of the High Eigenmodes of Spin Diffusion in Porous Media. Phys. Rev. Lett. 85:3878
36. Song Y., Ryu S., Sen P.N. (2000b) Determining multiple length scales in rocks. Nature 406, 178
37. Song Y. (2001) Pore sizes and pore connectivity in rocks using the effect of internal field. Mag. Reson. Img. 19, 417
38. Toumelin, E., Torres-Verdin, C., Chen, S.: Modeling of multiple echo-time NMR measurements for complex pore geometries and multiphase saturations. SPE 85635, 2002 SPE Annual Technical Conference and Exhibition, San Antonio, September 29-October 2
39. Valfouskaya A., Adler P.M., Thovert J.-F., Fleury M. (2005) Nuclear-magnetic-resonance diffusion simulations in porous media. J. Appl. Phys. 97:083510
40. Valfouskaya A., Adler P.M., Thovert J.-F., Fleury M. (2006) Nuclear magnetic resonance diffusion with surface relaxation in porous media. J. Coll. Int. Sci. 295, 188
41. Valfouskaya A., Adler P.M. (2005) Nuclear-magnetic-resonance diffusion simulations in two phases in porous media. Phys. Rev. E 72:056317
42. van Dijke M., Sorbie K. (2003) Three-phase capillary entry conditions in pores of noncircular cross-section. J. Colloid Interface Sci. 260, 385-397
43. Wilkinson D., Johnson D., Schwartz L. (1991) Nuclear magnetic relaxation in porous media: The role of the mean lifetime τ(ρ, D). Phys. Rev. B 44, 4960-4973
44. Zhang Q., Huang C., Hirasaki G. (2000) Interpretation of wettability in sandstones With NMR analysis. Petrophysics 41(3):223-233
45. Zielinski L.J., Song Y., Ryu S., Sen P.N. (2002) Characterization of coupled pore systems from the diffusion eigenspectrum. J. Chem. Phys. 117:5361